Deciding how to jointly schedule jobs and perform preventive maintenance is a fundamental problem in flexible manufacturing systems, particularly those arising in semiconductor manufacturing. At the same time, past work in this area shows that, even when there is only one station and one type of job, identifying policies that minimize the amount of work-in-process (WIP) is a difficult problem. In this paper, we study a single-station version of this problem with an arbitrary number of job classes, with the objective of minimizing average maintenance costs plus the weighted average amount of WIP. We identify conditions under which it suffices to schedule jobs according to both a server-state-dependent version of the cμ-rule, and a static cμ-rule where the average service rates are used. One of these conditions states that the ratio between the service rates should remain constant as the server deteriorates. When this assumption does not hold, scheduling with the cμ-rule can in fact lead to an unstable system; we illustrate this using a simple example. On the other hand, we also present numerical evidence that cμ-based scheduling performs well compared to other scheduling rules, and relative to a policy based on solving a Markov decision process.

中文翻译：

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动态调度和维护灵活的服务器

决定如何共同安排工作和执行预防性维护是柔性制造系统中的一个基本问题，尤其是在半导体制造中出现的那些问题。同时，该领域过去的工作表明，即使只有一个工作站和一种类型的工作，确定最小化在制品 (WIP) 数量的政策也是一个难题。在本文中，我们研究了该问题的单站版本，具有任意数量的作业类别，目标是最小化平均维护成本和加权平均在制品数量。我们根据cμ规则的依赖于服务器状态的版本和静态cμ来确定足以调度作业的条件- 使用平均服务费率的规则。这些条件之一表明，随着服务器的恶化，服务费率之间的比率应保持不变。当这个假设不成立时，使用cμ规则进行调度实际上会导致系统不稳定；我们用一个简单的例子来说明这一点。另一方面，我们还提供了数值证据表明基于cμ的调度与其他调度规则相比表现良好，并且相对于基于解决马尔可夫决策过程的策略。